Find the equation of the tangent line to the curve

Question

 at the given point. y=x^3-2x+1 at (3,22)?

Answer 1

The curve equation is y = x³ - 2x + 1

Differentiating on each side with respect of x .

y' = 3x² - 2

Substitute the values (x , y) = (3, 22) in above equation.

y' = 3(3)² - 2

y' = 27 - 2

y' = 25

This is the slope of tangent line to the parabola at (3, 22).

To find the tangent line equation, substitute the values of m = 25 and (x, y) = (3, 22) in the slope intercept form of an equation y = mx + b.

Where m is slope and b is y intercept.

22 = 25(3) + b

22 = 75 + b

b = - 75 + 22

b = - 53

Substitute m = 25 and b = - 53 in y = mx + b.

y = 25x - 53

Tangent line equation is y =  25x - 53.